Question: Solve for $x$ and $y$ using elimination. ${-2x+2y = 8}$ ${-5x+y = 0}$
Answer: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the bottom equation by $-2$ ${-2x+2y = 8}$ $10x-2y = 0$ Add the top and bottom equations together. $8x = 8$ $\dfrac{8x}{{8}} = \dfrac{8}{{8}}$ ${x = 1}$ Now that you know ${x = 1}$ , plug it back into $\thinspace {-2x+2y = 8}\thinspace$ to find $y$ ${-2}{(1)}{ + 2y = 8}$ $-2+2y = 8$ $-2{+2} + 2y = 8{+2}$ $2y = 10$ $\dfrac{2y}{{2}} = \dfrac{10}{{2}}$ ${y = 5}$ You can also plug ${x = 1}$ into $\thinspace {-5x+y = 0}\thinspace$ and get the same answer for $y$ : ${-5}{(1)}{ + y = 0}$ ${y = 5}$